How do you find f'(x) using the definition of a derivative for f(x)=7x2−3?

The derivative of f(x) with respect to x is defined as:limh→0[f(x+h)−f(x)h]limh→0(7(x+h)2−3−(7x2−3)h)limh→0(7(x+h)2−3−(7x2−3)h)=14xAnswer:=14x

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Aldo Fernandez

2022-04-18

How do you find f'(x) using the definition of a derivative for

f (x) = 7 x^{2} - 3

Latkaxu8j

Beginner2022-04-19Added 11 answers

The rules:
The derivative of a number is 0
The derivative of a power of x is power times x to power-1.
So if

g (x) = x^{2} \to g^{'} (x) = 2 \cdot x^{2 - 1} = 2 x

So here we get:
f'(x)=7*2x-0=14x
Result:
f'(x)=14x

enchantsyseq

Beginner2022-04-20Added 19 answers

The derivative of f(x) with respect to x is defined as:

lim_{h \to 0} [\frac{f (x + h) - f (x)}{h}]

lim_{h \to 0} (\frac{7 {(x + h)}^{2} - 3 - (7 x^{2} - 3)}{h})

lim_{h \to 0} (\frac{7 {(x + h)}^{2} - 3 - (7 x^{2} - 3)}{h}) = 14 x

Answer:
=14x

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